(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 10.4' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     17695,        606]
NotebookOptionsPosition[     12703,        456]
NotebookOutlinePosition[     15975,        544]
CellTagsIndexPosition[     15857,        538]
WindowTitle->ToDistribution
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[GridBox[{
   {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{
     Cell[BoxData[
      ActionMenuBox[
       FrameBox[
        InterpretationBox[Cell[TextData[{
          "See Also",
          StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
           StripOnInput->False]
         }]],
         TextCell[
          Row[{"See Also", 
            Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
        StripOnInput->False], {"\<\"PlusDistribution\"\>":>
       Documentation`HelpLookup["paclet:FeynCalc/ref/PlusDistribution"]},
       Appearance->None,
       MenuAppearance->Automatic,
       MenuStyle->"SeeAlso"]],
      LineSpacing->{1.4, 0}],
     "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\
\[ThickSpace]",
     Cell[BoxData[
      ActionMenuBox[
       FrameBox[
        InterpretationBox[Cell[TextData[{
          "URL",
          StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
           StripOnInput->False]
         }]],
         TextCell[
          Row[{"URL", 
            Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
        StripOnInput->False], {"\<\"FeynCalc/ref/ToDistribution\"\>":>
       None, "\<\"Copy Wolfram Documentation Center URL\"\>":>
       Module[{DocumentationSearch`Private`nb$}, 
        DocumentationSearch`Private`nb$ = NotebookPut[
           Notebook[{
             Cell["FeynCalc/ref/ToDistribution"]}, Visible -> False]]; 
        SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
        FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
        NotebookClose[DocumentationSearch`Private`nb$]; Null], 
       Delimiter, "\<\"Copy web URL\"\>":>
       Module[{DocumentationSearch`Private`nb$}, 
        DocumentationSearch`Private`nb$ = NotebookPut[
           Notebook[{
             Cell[
              BoxData[
               MakeBoxes[
                Hyperlink[
                "http://reference.wolfram.com/language/FeynCalc/ref/\
ToDistribution.html"], StandardForm]], "Input", TextClipboardType -> 
              "PlainText"]}, Visible -> False]]; 
        SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
        FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
        NotebookClose[DocumentationSearch`Private`nb$]; 
        Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{
         NotebookLocate[{
           URL[
            StringJoin[
             If[
              TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$273137], 
              "http://reference.wolfram.com/system-modeler/", 
              "http://reference.wolfram.com/language/"], 
             "FeynCalc/ref/ToDistribution", ".html"]], None}]}]},
       Appearance->None,
       MenuAppearance->Automatic,
       MenuStyle->"URLMenu"]],
      LineSpacing->{1.4, 0}]
    }], "AnchorBar"]}
  }]], "AnchorBarGrid",
 GridBoxOptions->{GridBoxItemSize->{"Columns" -> {
     Scaled[0.65], {
      Scaled[0.34]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
   "RowsIndexed" -> {}}},
 CellID->1],

Cell[TextData[{
 Cell["ToDistribution", "ObjectName"],
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{8, 0}],
    CacheGraphics->False],
   Spacer[8]]]],
 Cell[BoxData[""], "ObjectNameTranslation"]
}], "ObjectNameGrid"],

Cell[CellGroupData[{

Cell[BoxData[GridBox[{
   {"", Cell[TextData[{
     Cell[BoxData[
      RowBox[{"ToDistribution", "[", 
       RowBox[{"exp", ",", "x"}], "]"}]], "InlineFormula"],
     " \[LineSeparator]",
     "replaces (1-x)^(a Epsilon - 1) in exp by 1/(a Epsilon) \
DeltaFunction[1-x] + 1/(1-x) + a Epsilon Log[1-x]/(1-x) + 1/2 a^2 Epsilon^2 \
Log[1-x]^2/(1-x)] and (1-x)^(a Epsilon - 2) in exp by -1/(a Epsilon) \
DeltaFunctionPrime[1-x] + 1/(1-x)^2 + (a Epsilon) Log[1-x]/(1-x)^2 + a^2 \
Epsilon^2/2 Log[1-x]^2/(1-x)^2 + a^3 Epsilon^3/6 Log[1-x]^3/(1-x)^2."
    }]]}
  }]], "Usage",
 GridBoxOptions->{
 GridBoxBackground->{
  "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, 
   "RowsIndexed" -> {}}},
 CellID->982511436],

Cell[CellGroupData[{

Cell[TextData[Cell[BoxData[
 ButtonBox[Cell[TextData[{
   Cell[BoxData[
    InterpretationBox[
     StyleBox[
      GraphicsBox[{},
       BaselinePosition->Baseline,
       ImageSize->{6, 0}],
      CacheGraphics->False],
     Spacer[6]]]],
   "Details"
  }], "NotesFrameText"],
  Appearance->{Automatic, None},
  BaseStyle->None,
  ButtonFunction:>(FrontEndExecute[{
     FrontEnd`SelectionMove[
      FrontEnd`SelectedNotebook[], All, ButtonCell], 
     FrontEndToken["OpenCloseGroup"], 
     FrontEnd`SelectionMove[
      FrontEnd`SelectedNotebook[], After, CellContents]}]& ),
  Evaluator->None,
  Method->"Preemptive"]]]], "NotesSection",
 WholeCellGroupOpener->True,
 CellGroupingRules->{"SectionGrouping", 50},
 CellID->1231523278],

Cell["", "SectionHeaderSpacer"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Options", "[", "ToDistribution", "]"}]], "Input",
 CellTags->"ToDistribution",
 CellLabel->"In[1]:=",
 CellID->1833387073],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{"PlusDistribution", "\[Rule]", "Identity"}], "}"}], 
  TraditionalForm]], "Output",
 ImageSize->{172, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"ToDistribution",
 CellLabel->"Out[1]=",
 CellID->1934939097]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "PrimaryExamplesSection",
 WholeCellGroupOpener->True,
 CellTags->"PrimaryExamplesSection",
 CellID->1972955354],

Cell[CellGroupData[{

Cell[TextData[{
 "Basic Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "ExampleSection", "ExampleSection",
 WholeCellGroupOpener->True,
 CellID->747089580],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ToDistribution", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{"1", "-", "x"}], ")"}], "^", 
    RowBox[{"(", 
     RowBox[{"Epsilon", "-", "1"}], ")"}]}], ",", "x", ",", 
   RowBox[{"PlusDistribution", "\[Rule]", "pd"}]}], "]"}]], "Input",
 CellTags->"ToDistribution",
 CellLabel->"In[1]:=",
 CellID->1094502312],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    FractionBox["1", "6"], " ", 
    SuperscriptBox[
     TagBox["\[CurlyEpsilon]",
      TraditionalForm], "3"], " ", 
    RowBox[{"pd", "(", 
     FractionBox[
      RowBox[{
       SuperscriptBox["log", "3"], "(", 
       RowBox[{"1", "-", "x"}], ")"}], 
      RowBox[{"1", "-", "x"}]], ")"}]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    SuperscriptBox[
     TagBox["\[CurlyEpsilon]",
      TraditionalForm], "2"], " ", 
    RowBox[{"pd", "(", 
     FractionBox[
      RowBox[{
       SuperscriptBox["log", "2"], "(", 
       RowBox[{"1", "-", "x"}], ")"}], 
      RowBox[{"1", "-", "x"}]], ")"}]}], "+", 
   RowBox[{
    TagBox["\[CurlyEpsilon]",
     TraditionalForm], " ", 
    RowBox[{"pd", "(", 
     FractionBox[
      RowBox[{"log", "(", 
       RowBox[{"1", "-", "x"}], ")"}], 
      RowBox[{"1", "-", "x"}]], ")"}]}], "+", 
   RowBox[{"pd", "(", 
    FractionBox["1", 
     RowBox[{"1", "-", "x"}]], ")"}], "+", 
   FractionBox[
    RowBox[{"\[Delta]", "(", 
     FormBox[
      RowBox[{"1", "-", "x"}],
      TraditionalForm], ")"}], 
    TagBox["\[CurlyEpsilon]",
     TraditionalForm]]}], TraditionalForm]], "Output",
 ImageSize->{319, 82},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"ToDistribution",
 CellLabel->"Out[1]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ToDistribution", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{"1", "-", "x"}], ")"}], "^", 
    RowBox[{"(", 
     RowBox[{"Epsilon", "-", "2"}], ")"}]}], ",", "x", ",", 
   RowBox[{"PlusDistribution", "\[Rule]", "Identity"}]}], "]"}]], "Input",
 CellTags->"ToDistribution",
 CellLabel->"In[2]:=",
 CellID->1034527004],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"-", 
    FractionBox[
     RowBox[{
      SuperscriptBox["\[Delta]", "\[Prime]"], "(", 
      FormBox[
       RowBox[{"1", "-", "x"}],
       TraditionalForm], ")"}], 
     TagBox["\[CurlyEpsilon]",
      TraditionalForm]]}], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      TagBox["\[CurlyEpsilon]",
       TraditionalForm], "3"], " ", 
     RowBox[{
      SuperscriptBox["log", "3"], "(", 
      RowBox[{"1", "-", "x"}], ")"}]}], 
    RowBox[{"6", " ", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"1", "-", "x"}], ")"}], "2"]}]], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      TagBox["\[CurlyEpsilon]",
       TraditionalForm], "2"], " ", 
     RowBox[{
      SuperscriptBox["log", "2"], "(", 
      RowBox[{"1", "-", "x"}], ")"}]}], 
    RowBox[{"2", " ", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"1", "-", "x"}], ")"}], "2"]}]], "+", 
   FractionBox[
    RowBox[{
     TagBox["\[CurlyEpsilon]",
      TraditionalForm], " ", 
     RowBox[{"log", "(", 
      RowBox[{"1", "-", "x"}], ")"}]}], 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"1", "-", "x"}], ")"}], "2"]], "+", 
   FractionBox["1", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{"1", "-", "x"}], ")"}], "2"]]}], TraditionalForm]], "Output",
 ImageSize->{479, 43},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"ToDistribution",
 CellLabel->"Out[2]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Series2", "[", 
  RowBox[{
   RowBox[{"Integrate", "[", 
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"1", "-", "x"}], ")"}], 
      RowBox[{"Epsilon", "-", "2"}]], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "0", ",", "1"}], "}"}], ",", 
     RowBox[{"GenerateConditions", "\[Rule]", "False"}]}], "]"}], ",", 
   "Epsilon", ",", "3"}], "]"}]], "Input",
 CellTags->"ToDistribution",
 CellLabel->"In[3]:=",
 CellID->941654875],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"-", 
    SuperscriptBox[
     TagBox["\[CurlyEpsilon]",
      TraditionalForm], "3"]}], "-", 
   SuperscriptBox[
    TagBox["\[CurlyEpsilon]",
     TraditionalForm], "2"], "-", 
   TagBox["\[CurlyEpsilon]",
    TraditionalForm], "-", "1"}], TraditionalForm]], "Output",
 ImageSize->{113, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"ToDistribution",
 CellLabel->"Out[3]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{"ToDistribution", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"(", 
       RowBox[{"1", "-", "x"}], ")"}], "^", 
      RowBox[{"(", 
       RowBox[{"Epsilon", "-", "2"}], ")"}]}], ",", "x"}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"ToDistribution",
 CellLabel->"In[4]:=",
 CellID->1539995997],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"-", 
    SuperscriptBox[
     TagBox["\[CurlyEpsilon]",
      TraditionalForm], "3"]}], "-", 
   SuperscriptBox[
    TagBox["\[CurlyEpsilon]",
     TraditionalForm], "2"], "-", 
   TagBox["\[CurlyEpsilon]",
    TraditionalForm], "-", "1"}], TraditionalForm]], "Output",
 ImageSize->{113, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"ToDistribution",
 CellLabel->"Out[4]="]
}, Open  ]]
}, Open  ]],

Cell["", "SectionFooterSpacer"]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "See Also"
}], "SeeAlsoSection",
 WholeCellGroupOpener->True,
 CellID->1255426704],

Cell[TextData[{
 StyleBox[ButtonBox["PlusDistribution",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/PlusDistribution",
  ButtonNote->"PlusDistribution"],
  FontFamily->"Verdana"],
 "."
}], "SeeAlso"]
}, Open  ]],

Cell[" ", "FooterCell"]
},
Saveable->False,
ScreenStyleEnvironment->"Working",
WindowSize->{725, 750},
WindowMargins->{{-10, Automatic}, {Automatic, -8}},
WindowTitle->"ToDistribution",
TaggingRules->{
 "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> 
  GridBox[{{
      RowBox[{
        ButtonBox[
        "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", 
         BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> 
    Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> 
  None, "RootCaptions" -> "", 
  "Metadata" -> {
   "built" -> "{2020, 6, 20, 19, 11, 59.760196}", 
    "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", 
    "keywords" -> {}, "specialkeywords" -> {}, 
    "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> 
    "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> 
    "None", "summary" -> 
    "ToDistribution[exp, x] replaces (1-x)^(a Epsilon - 1) in exp by 1/(a \
Epsilon) DeltaFunction[1-x] + 1/(1-x) + a Epsilon Log[1-x]/(1-x) + 1/2 a^2 \
Epsilon^2 Log[1-x]^2/(1-x)] and (1-x)^(a Epsilon - 2) in exp by -1/(a \
Epsilon) DeltaFunctionPrime[1-x] + 1/(1-x)^2 + (a Epsilon) Log[1-x]/(1-x)^2 + \
a^2 Epsilon^2/2 Log[1-x]^2/(1-x)^2 + a^3 Epsilon^3/6 Log[1-x]^3/(1-x)^2.", 
    "synonyms" -> {}, "tabletags" -> {}, "title" -> "ToDistribution", 
    "titlemodifier" -> "", "windowtitle" -> "ToDistribution", "type" -> 
    "Symbol", "uri" -> "FeynCalc/ref/ToDistribution"}, "SearchTextTranslated" -> 
  ""},
CellContext->"Global`",
FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)",
StyleDefinitions->Notebook[{
   Cell[
    StyleData[
    StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], 
   Cell[
    StyleData["Input"], CellContext -> "Global`"], 
   Cell[
    StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, 
  FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", 
  StyleDefinitions -> "Default.nb"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
 "ToDistribution"->{
  Cell[5499, 163, 146, 4, 70, "Input",
   CellTags->"ToDistribution",
   CellID->1833387073],
  Cell[5648, 169, 295, 10, 37, "Output",
   CellTags->"ToDistribution",
   CellID->1934939097],
  Cell[6637, 215, 351, 11, 27, "Input",
   CellTags->"ToDistribution",
   CellID->1094502312],
  Cell[6991, 228, 1332, 47, 103, "Output",
   CellTags->"ToDistribution"],
  Cell[8360, 280, 357, 11, 27, "Input",
   CellTags->"ToDistribution",
   CellID->1034527004],
  Cell[8720, 293, 1465, 53, 64, "Output",
   CellTags->"ToDistribution"],
  Cell[10222, 351, 478, 15, 54, "Input",
   CellTags->"ToDistribution",
   CellID->941654875],
  Cell[10703, 368, 456, 16, 37, "Output",
   CellTags->"ToDistribution"],
  Cell[11196, 389, 427, 14, 27, "Input",
   CellTags->"ToDistribution",
   CellID->1539995997],
  Cell[11626, 405, 456, 16, 37, "Output",
   CellTags->"ToDistribution"]},
 "PrimaryExamplesSection"->{
  Cell[6004, 186, 388, 15, 31, "PrimaryExamplesSection",
   CellTags->"PrimaryExamplesSection",
   CellID->1972955354]}
 }
*)
(*CellTagsIndex
CellTagsIndex->{
 {"ToDistribution", 14815, 504},
 {"PrimaryExamplesSection", 15713, 531}
 }
*)
(*NotebookFileOutline
Notebook[{
Cell[586, 21, 3043, 74, 53, "AnchorBarGrid",
 CellID->1],
Cell[3632, 97, 291, 11, 45, "ObjectNameGrid"],
Cell[CellGroupData[{
Cell[3948, 112, 728, 17, 136, "Usage",
 CellID->982511436],
Cell[CellGroupData[{
Cell[4701, 133, 739, 24, 31, "NotesSection",
 CellGroupingRules->{"SectionGrouping", 50},
 CellID->1231523278],
Cell[5443, 159, 31, 0, 70, "SectionHeaderSpacer"],
Cell[CellGroupData[{
Cell[5499, 163, 146, 4, 70, "Input",
 CellTags->"ToDistribution",
 CellID->1833387073],
Cell[5648, 169, 295, 10, 37, "Output",
 CellTags->"ToDistribution",
 CellID->1934939097]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[6004, 186, 388, 15, 31, "PrimaryExamplesSection",
 CellTags->"PrimaryExamplesSection",
 CellID->1972955354],
Cell[CellGroupData[{
Cell[6417, 205, 195, 6, 26, "ExampleSection",
 CellID->747089580],
Cell[CellGroupData[{
Cell[6637, 215, 351, 11, 27, "Input",
 CellTags->"ToDistribution",
 CellID->1094502312],
Cell[6991, 228, 1332, 47, 103, "Output",
 CellTags->"ToDistribution"]
}, Open  ]],
Cell[CellGroupData[{
Cell[8360, 280, 357, 11, 27, "Input",
 CellTags->"ToDistribution",
 CellID->1034527004],
Cell[8720, 293, 1465, 53, 64, "Output",
 CellTags->"ToDistribution"]
}, Open  ]],
Cell[CellGroupData[{
Cell[10222, 351, 478, 15, 54, "Input",
 CellTags->"ToDistribution",
 CellID->941654875],
Cell[10703, 368, 456, 16, 37, "Output",
 CellTags->"ToDistribution"]
}, Open  ]],
Cell[CellGroupData[{
Cell[11196, 389, 427, 14, 27, "Input",
 CellTags->"ToDistribution",
 CellID->1539995997],
Cell[11626, 405, 456, 16, 37, "Output",
 CellTags->"ToDistribution"]
}, Open  ]]
}, Open  ]],
Cell[12109, 425, 31, 0, 29, "SectionFooterSpacer"]
}, Open  ]],
Cell[CellGroupData[{
Cell[12177, 430, 270, 12, 31, "SeeAlsoSection",
 CellID->1255426704],
Cell[12450, 444, 211, 7, 56, "SeeAlso"]
}, Open  ]],
Cell[12676, 454, 23, 0, 41, "FooterCell"]
}
]
*)

(* End of internal cache information *)

